The present invention relates to a method for producing a ceramic diaphragm structure which is used as a constitutional member of various kinds of sensors, piezoelectric/electrostrictive actuators, or the like.
A ceramic diaphragm structure has a structure in which a thin and flexible diaphragm plate is superposed on a substrate having at least one window portion so as to cover the window portion and to work as a diaphragm. Such a ceramic diaphragm structure is used for various kinds of sensors by being constituted so that a diaphragm portion detects a bending displacement originated from a subject to be measured by an adequate means, or used as a constituting member of a piezoelectric/electrostrictive actuator by being constituted so that a pressure is given to the pressure room formed inside the actuator by deformation of the diaphragm portion due to a piezoelectric/electrostrictive element.
A ceramic diaphragm structure is produced by unitarily superposing a thin ceramic green sheet (hereinafter referred to as a green sheet) on a ceramic green substrate (hereinafter referred to as a green substrate) to obtain a laminate, and subsequently firing the laminate. After firing, the green substrate becomes a substrate, and the green sheet becomes a diaphragm plate. Generally, there is used a ceramic diaphragm structure 3 having a diaphragm portion 1 formed to have a protrudent shape toward the side opposite to a window portion 8 of a substrate 2 as shown in FIG. 1, so as to prevent a crack or a depression in a firing step. Such a diaphragm portion 1 having a protrudent shape as described above can have a higher inherent resonance frequency in comparison with a diaphragm portion having a flat shape. Further, it is recognized that a diaphragm portion having a protrudent shape is excellent in mechanical strength and is not hindered upon sintering a film formed on the surface of the diaphragm portion 1.
In the fields of sensor and piezoelectric/electrostrictive actuator, since a demand for high precision and densification is raised, it is required to make a diaphragm portion more minute or to increase the number of the diaphragm portions.
When a ceramic diaphragm structure having a protrudent shape is produced, there are used materials which satisfy the following formulae 1), 2), and 3):
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
xe2x80x83S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate) and S(sheet) denote shrinkage rates(%) of the ceramic green substrate and the ceramic green sheet, respectively, and T70(substrate) and T70(sheet) denote mid-sintering temperatures (xc2x0 C.) of the ceramic green substrate and the ceramic green sheet, respectively.).
JP-A-8-51238 discloses that by using such a material, a protrusion can be made in a green sheet (diaphragm plate) toward the side opposite to a window portion arranged in a substrate during firing without any crack or the like. That is, a thin ceramic portion having a protrudent shape can be formed by setting differences in shrinkage rate and mid-sintering temperature between a green substrate and a green sheet.
Incidentally, a shrinkage rate (%) means a shrinkage rate (%), in a direction of a surface, of a green substrate and a green sheet independently fired at the same temperature as the temperature at which a laminate is fired, and the shrinkage rate (%) is shown by {(length before firingxe2x88x92length after firing)/length before firing}xc3x97100(%). The term xe2x80x9ca direction of surfacexe2x80x9d does not mean the direction of thickness, but means a predetermined direction on the surface where a green substrate or a green sheet is molded. A mid-sintering temperature means a firing temperature at which a shrinkage reaches 70% of the aforementioned shrinkage rate, S(substrate) and S(sheet) in a firing step, and a mid-sintering temperature is a barometer showing a sintering speed.
However, the method disclosed in JP-A-8-51238 is on the supposition that a shrinkage rate and a mid-sintering temperature of a green substrate are uniform from a portion near a green sheet to a portion apart from the green sheet. However, in this method, as shown in FIG. 2, a ceramic diaphragm structure 3 is constituted of a substrate 2 and a diaphragm plate 12, and a plurality of the ceramic diaphragm structures 3 constitutes a ceramic plate 15. Therefore, a diaphragm structure has a large waviness, and a warpage is caused wholly in a ceramic plate including diaphragm structures.
It is difficult to reform the aforementioned warpage and waviness even if the ceramic substrate is subjected to firing again with loading. When a load on the ceramic plate is too large, a diaphragm portion 1 and/or a substrate 2 damage(s). When a warpage or a waviness is left as it is, dimensional preciseness of a diaphragm structure 3 deteriorates, and therefore, preciseness in printing of a film pattern on a diaphragm plate deteriorates, and/or variance in thickness of a film formed on the diaphragm plate is caused. Accordingly, when such a diaphragm structure is used for a sensor, such a sensor brings deviation in detection preciseness, and when it is used for a piezoelectric/electrostrictive actuator, such an actuator brings deterioration or variance in displacement.
As a result of the various studies, the present inventors proposed, in JP-A-10-117024, the following method as a method for producing a ceramic diaphragm structure, which can form a diaphragm portion having a protrusion toward the side opposite to a window portion of a substrate and which can advantageously reduce a waviness of a diaphragm structure and/or a warpage of a ceramic plate including the diaphragm structures.
First, we proposed a method for producing a ceramic diaphragm structure, comprising the steps of:
superposing a thin ceramic green sheet having at least one layer on a ceramic green substrate having at least one window portion and at least one layer so as to cover the window portion to obtain a unitary laminate, and
firing the unitary laminate so that a diaphragm portion has a protrusion toward a side opposite to the window portion;
wherein the ceramic green substrate and the ceramic green sheet satisfy the formulae:
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate), and S(sheet) denote shrinkage rates (%) of the ceramic green substrate and the ceramic green sheet, respectively, and T70(substrate) and T70(sheet) denote mid-sintering temperatures (xc2x0 C.) of the ceramic green substrate and the ceramic green sheet, respectively.), and an average sintering temperature difference of the layers of the ceramic green substrate, shown by the following formula, is larger than 0:       4    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                                        T            70                    ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N denotes the number of layers constituting the ceramic green substrate, T70(substrate)n denotes a mid-sintering temperature (xc2x0 C.) of a layer positioned in the nth place from the bottom of the laminate in the ceramic green substrate having the ceramic green sheet thereon, tn and tn+1 denote distances from the lower and upper surfaces, respectively, of the layer positioned in the nth place to a neutral line of the substrate after firing the unitary laminate, using (xe2x88x92) for a surface under the neutral line and (+) for a surface over the neutral line.).
Secondly, the inventors proposed a method for producing a ceramic diaphragm structure, comprising the steps of:
superposing a thin ceramic green sheet having at least one layer on a ceramic green substrate having at least one window portion and at least one layer so as to cover the window portion to obtain a unitary laminate, and firing the unitary laminate so that a diaphragm portion has a protrusion toward a side opposite to the window portion;
wherein the ceramic green substrate and the ceramic green sheet satisfy the aforementioned formulae 1), 2) and 3) (hereinafter the same thing is applicable to them), i.e.,:
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate), and S(sheet) denote shrinkage rates (%) of the ceramic green substrate and the ceramic green sheet, respectively, T70(substrate) and T70(sheet) denote mid-sintering temperatures (xc2x0 C.) of the ceramic green substrate and the ceramic green sheet, respectively.), and an average shrinkage-rate difference of the layers of the ceramic green substrate, shown by the following formula 5), is larger than 0;       5    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                            S          ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N denotes the number of layers constituting the ceramic green substrate, S(substrate)n denotes a shrinkage rate (%) of a layer positioned in the nth place from the bottom of the laminate in the ceramic green substrate having the ceramic green sheet thereon, and tn and tn+1 donote distances from the lower and upper surfaces, respectively, of the layer positioned in the nth place to a neutral line of the substrate after firing the unitary laminate, using (xe2x88x92) for a surface under the neutral line and (+) for a surface over the neutral line.).
In other words, in the method for producing a ceramic diaphragm structure disclosed by JP-A-10-117024, firing is conducted under a condition that an average mid-sintering temperature difference shown by the formula 4) is larger then 0 or that an average shrinkage-rate difference shown by the formula 5) is larger than 0.
Specifically, as embodiments for the aforementioned methods, there are 5 kinds of embodiments in which desired ceramic diaphragm structures are produced by firing under a condition that both an average mid-sintering temperature difference shown by the formula 4) and an average shrinkage-rate difference shown by the formula 5) are larger than 0, that an average mid-sintering temperature difference is larger than 0 and an average shrinkage-rate difference is equal to 0 or smaller than 0, or that an average shrinkage-rate difference is larger than 0 and an average mid-sintering temperature difference is equal to 0 or smaller than 0.
However, even if firing is conducted under the aforementioned conditions, there is sometimes observed a phenomenon of partial distortion or deformation in a protrudent shape of a diaphragm portion, or unevenness in protrudent shape between adjacent diaphragm portions which are formed in series. Unevenness in protrudent shape is sometimes observed among a plurality of diaphragm structures which are disposed on a ceramic plate.
In the course of various investigation, it has been found that such a phenomenon is generated with high frequency as a diaphragm portion become finer and as the number of diaphragm portions to be formed is increased.
Therefore, the present invention aims to provide a method for producing a ceramic diaphragm structure in which protrudent shape of the diaphragm portion is not deformed, distorted, or uneven in the firing process.
As a result of various investigation, we have found that the aforementioned problems can be solved by the firing under a condition that an average mid-sintering temperature difference shown by the formula 4) is smaller than 0 and/or an average shrinkage-rate difference shown by the formula 5) is smaller than 0 with an approach which is different from the method disclosed by the aforementioned JP-A-10-117024 as a method for suppressing deformation, distortion, or unevenness in a protrudent shape of a diaphragm portion with resignation to generation of warpage and waviness in a ceramic plate including the diaphragm structures to a certain degree. Particularly, we have found that, when a warpage (including waviness) upon firing a ceramic plate is not larger than 10 mm, such a warpage (waviness) can be sufficiently corrected by firing again the ceramic plate, under a suitable load, at a temperature of 1200xc2x0 C.-1700xc2x0 C., preferable about the same temperature as the temperature at which the ceramic plate was fired and that deformation, distortion, or unevenness in a protrudent shape of a diaphragm portion can be suppressed by conduct firing under the aforementioned conditions. Thus, the present invention has been accomplished based on the above-mentioned findings.
A method for producing a ceramic diaphragm structure according to the present invention are classified into the following 4 embodiments. That is,
1) An average mid-sintering temperature difference shown by the formula 4) is smaller than 0, and an average shrinkage-rate difference shown by the formula 5) is smaller than 0.
2) An average mid-sintering temperature difference shown by the formula 4) is 0, and an average shrinkage-rate difference shown by the formula 5) is smaller than 0.
3) An average mid-sintering temperature difference shown by the formula 4) is smaller than 0, and an average shrinkage-rate difference shown by the formula 5) is 0.
4) One of an average mid-sintering temperature difference shown by the formula 4) and an average shrinkage-rate difference shown by the formula 5) is larger than 0, and the other is smaller than 0, and the value given by the following formula 6):             6      )        ⁢          xe2x80x83        ⁢                  ∑                  n          =          1                N            ⁢                                                  T              70                        ⁡                          (              substrate              )                                n                ⁢                              ∫            tn                          tn              +              1                                ⁢                      xc3x97                          ⅆ              x                                            +      16.8    xc3x97                  ∑                  n          =          1                N            ⁢                                    S            ⁡                          (              substrate              )                                n                ⁢                              ∫            tn                          tn              +              1                                ⁢                      xc3x97                          ⅆ              x                                          
(wherein N, S(substrate)n, T70(substrate)n, tn, and tn+1 denote as mentioned above.) is smaller than 0.
The aforementioned embodiments 1)-4) include an embodiment which satisfies the following formula 7):                     7        )            ⁢              xe2x80x83            ⁢                        ∑                      n            =            1                    N                ⁢                                                            T                70                            ⁡                              (                substrate                )                                      n                    ⁢                                    ∫              tn                              tn                +                1                                      ⁢                          xc3x97                              ⅆ                x                                                          +          16.8      xc3x97                        ∑                      n            =            1                    N                ⁢                                            S              ⁡                              (                substrate                )                                      n                    ⁢                                    ∫              tn                              tn                +                1                                      ⁢                          xc3x97                              ⅆ                x                                                           greater than             -      15        ⁢                  {                              (                                          t                                  N                  +                  1                                            -                              t                1                                      )                    /          2                }            2      
(wherein N, S(substrate)n, T70(substrate)n, tn, and tn+1 denote as mentioned above, t1 denotes, using (xe2x88x92), a distance from a lower surface of a lowest layer of the substrate to a neutral line of the substrate after the unitary laminate is fired, and tN+1 denotes, using (+), a distance from an upper surface of the layer positioned in number N place from the lowest layer of the substrate to the neutral line of the substrate after the unitary laminate is fired.).
That is, as a first embodiment of the present invention, there is provided a method for forming a ceramic diaphragm structure comprising the steps of:
a) providing a laminate, comprising:
i) a ceramic green substrate having at least one window therethrough and a plurality of layers; and
ii) a thin ceramic green sheet having at least one layer superposed on the ceramic green substrate to cover the at least one window; and
b) firing the laminate so that the ceramic green sheet provides a diaphragm portion protruding in a direction away from the at least one window;
wherein the ceramic green substrate and the ceramic green sheet satisfy the aforementioned formulae 1), 2) and 3), i.e.,:
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate) and S(sheet) denote shrinkage rates(%) of the ceramic green substrate and the ceramic green sheet, respectively, and T70(substrate) and T70(sheet) denote mid-sintering temperatures (xc2x0 C.) of the ceramic green substrate and the ceramic green sheet, respectively.), and an average mid-sintering temperature difference of the ceramic green substrate, shown by the following formula, is smaller than 0:       4    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                                        T            70                    ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N denotes the number of layers constituting the ceramic green substrate, T70(substrate)n denotes a mid-sintering temperature (xc2x0 C.) of a layer positioned in the nth place from the bottom of the laminate in the ceramic green substrate having the ceramic green sheet thereon, tn and tn+1 denote distances from the lower and upper surfaces, respectively, of the layer positioned in the nth place to a neutral line of the substrate after firing the unitary laminate, using (xe2x88x92) for a surface under the neutral line and (+) for a surface over the neutral line.), and an average shrinkage-rate difference of the ceramic green substrate, shown by the following formula, is smaller than 0:       5    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                            S          ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, tn, and tn+1 denote as described above, and S(substrate)n denotes a shrinkage rate (%) of a layer positioned in the nth place from the bottom of the laminate in the ceramic green substrate having the ceramic green sheet thereon.).
As a second embodiment of the present invention, there is provided a method for forming a ceramic diaphragm structure comprising the steps of:
a) providing a laminate, comprising:
i) a ceramic green substrate having at least one window therethrough and a plurality of layers; and
ii) a thin ceramic green sheet having at least one layer superposed on the ceramic green substrate to cover the at least one window; and
b) firing the laminate so that the ceramic green sheet provides a diaphragm portion protruding in a direction away from the at least one window;
wherein the ceramic green substrate and the ceramic green sheet satisfy the formulae 1), 2), and 3):
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate), and S(sheet), T70(substrate), and T70(sheet) denote as described above.) and an average mid-sintering temperature difference of the ceramic green substrate, shown by the following formula, is 0:       4    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                                        T            70                    ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, T70(substrate)n, tn, and tn+1 denote as described above.), and an average shrinkage-rate difference of the ceramic green substrate, shown by the formula, is smaller than 0:       5    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                            S          ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, S(substrate)n, tn, and tn+1 denote as described above.).
As a third embodiment of the present invention, there is provided a method for forming a ceramic diaphragm structure comprising the steps of:
a) providing a laminate, comprising:
i) a ceramic green substrate having at least one window therethrough and a plurality of layers; and
ii) a thin ceramic green sheet having at least one layer superposed on the ceramic green substrate to cover the at least one window; and
b) firing the laminate so that the ceramic green sheet provides a diaphragm portion protruding in a direction away from the at least one window;
wherein the ceramic green substrate and the ceramic green sheet satisfy the formulae:
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate), S(sheet), T70(substrate), and T70(sheet) denote as described above.), and average mid-sintering temperature difference of the ceramic green substrate, shown by the following formula 4), is smaller than 0:       4    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                                        T            70                    ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, T70(substrate)n, tn, and tn+1 denote as described above.), and an average shrinkage-rate difference of the ceramic green substrate, shown by the formula 5), is 0:       5    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                            S          ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, S(substrate)n, tn, and tn+1 denote as described above.).
As a fourth embodiment of the present invention, there is provided a method for forming a ceramic diaphragm structure comprising the steps of:
a) providing a laminate, comprising:
i) a ceramic green substrate having at least one window therethrough and a plurality of layers; and
ii) a thin ceramic green sheet having at least one layer superposed on the ceramic green substrate to cover the at least one window; and
b) firing the laminate so that the ceramic green sheet provides a diaphragm portion protruding in a direction away from the at least one window;
wherein the ceramic green substrate and the ceramic green sheet satisfy the formulae:
S(substrate)xe2x88x92S(sheet)xe2x89xa7xe2x88x920.08{T70(substrate)xe2x88x92T70(sheet)}xe2x88x921xe2x80x83xe2x80x831)
0xe2x89xa6T70(substrate)xe2x88x92T70(sheet)xe2x89xa6300,xe2x80x83xe2x80x832)
and
S(substrate)xe2x88x92S(sheet)xe2x89xa620xe2x80x83xe2x80x833)
(wherein S(substrate), S(sheet), T70(substrate), and T70(sheet) denote as described above.), and one of an average mid-sintering temperature difference of the ceramic green substrate, shown by the following formula 4):       4    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                                        T            70                    ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, T70(substrate)n, tn, and tn+1 denote as described above.), and an average shrinkage-rate difference of the ceramic green substrate, shown by the formula 5):       5    )    ⁢      xe2x80x83    ⁢            ∑              n        =        1            N        ⁢                            S          ⁡                      (            substrate            )                          n            ⁢                        ∫          tn                      tn            +            1                          ⁢                  xc3x97                      ⅆ            x                              
(wherein N, S(substrate)n, tn, and tn+1 denote as described above.), is smaller than 0, and the other is larger than 0, and a value of the ceramic green substrate, given by the following formula 6), is smaller than 0:             6      )        ⁢          xe2x80x83        ⁢                  ∑                  n          =          1                N            ⁢                                                  T              70                        ⁡                          (              substrate              )                                n                ⁢                              ∫            tn                          tn              +              1                                ⁢                      xc3x97                          ⅆ              x                                            +      16.8    xc3x97                  ∑                  n          =          1                N            ⁢                                    S            ⁡                          (              substrate              )                                n                ⁢                              ∫            tn                          tn              +              1                                ⁢                      xc3x97                          ⅆ              x                                          
(wherein N, S(substrate)n, T70(substrate)n, tn, and tn+1 denote as described above.).
As described above, each of the aforementioned four embodiments of the present invention includes an embodiment satisfying the following formula 7):                     7        )            ⁢              xe2x80x83            ⁢                        ∑                      n            =            1                    N                ⁢                                                            T                70                            ⁡                              (                substrate                )                                      n                    ⁢                                    ∫              tn                              tn                +                1                                      ⁢                          xc3x97                              ⅆ                x                                                          +          16.8      xc3x97                        ∑                      n            =            1                    N                ⁢                                            S              ⁡                              (                substrate                )                                      n                    ⁢                                    ∫              tn                              tn                +                1                                      ⁢                          xc3x97                              ⅆ                x                                                           greater than             -      15        ⁢                  {                              (                                          t                                  N                  +                  1                                            -                              t                1                                      )                    /          2                }            2      
(wherein N, S(substrate)n, T70(substrate)n, tn and tn+1 denote as described above, t1 denotes, using (xe2x88x92), a distance from a lower surface of a lowest layer of the substrate to a neutral line of the substrate after the unitary laminate is fired, and tN+1 denotes, using (+), a distance from an upper surface of the layer positioned in number N place from the lowest layer of the substrate to the neutral line of the substrate after the unitary laminate is fired.).